Question

What is the value of x? Enter your answer as a decimal.
Triangle M N P with segment A B parallel to segment N P and A is between M and N and B is between M and P. M N equals 46.2 centimeters, A N equals 14 centimeters, M P equals 72.6 centimeters, and M B equals x.

Answer 1

$\textbf{Concept used:}$

$\textbf{Basic proportionality theorem(Thales theorem):}$

$\text{If a line is drawn parallel to one side of a}$

$\text{triangle then it cuts other two sides proportionally.}$

$\textbf{Given: MN=46.2 cm, AN=14 cm, MP=72 cm}$

$\textbf{To find: x}$

$\text{In \triangle MNP, AB \parallel NP}$

$\text{By Thales theorem,}$

$\displaystyle\frac{AM}{AN}=\frac{BM}{BP}$

$\displaystyle\frac{46.2-14}{14}=\frac{x}{72-x}$

$\displaystyle\frac{32.2}{14}=\frac{x}{72-x}$

$\displaystyle\frac{16.1}{7}=\frac{x}{72-x}$

$16.1(72-x)=7x$

$1159.2-16.1x=7x$

$1159.2=7x+16.1x$

$1159.2=23.1x$

$\implies\;x=\frac{1159.2}{23.1}$

$\implies\bf\;x=50.18\;\text{cm}$

$\therefore\textbf{The value of x is 50.18 cm}$

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